Lecture 24: Applications of Valence Bond Theory The material in this lecture covers the following in Atkins.

14 Molecular structure Valence-bond theory 14.2 Homonuclear Diatomic Molecules 14.3 Polyatomic Molecules Lecture on-line Applications of Valence Bond Theory (PowerPoint) Applications of valence Bond Theory (PDF)

Handout for this lecture

H H

Valence Bond Theory Applications

A =1sH;B =1sHσ-bond: invarient to rotation

I. Diatomics

A B

ξ(1,2) =[A(1)B(2)+A(2)B(1)]×[α(1)β(2)−β(1)α(2)]

In general we write ψ(re,RN)as the product of electron pairfunctions ωi(r2i−1,r2i) as

ψ(re,RN) = ω1(r1,r2 ) × ω2(r3,r4 ) ×..ωi(r2i−1,r2i) × ωj(r2j−1,r2j).. × ωn(r2n−1,r2n)

Pair 1Pair 2

Pair i Pair jPair n

H Cl

Applicationsξ(1,2) =[A(1)B(2)+A(2)B(1)]×[α(1)β(2)−β(1)α(2)]

σ+sp(B) :

12

[3s+3pz]

Valence Bond Theory

Atomic orbitals on H (Hydrogen)

1sH

Atomic orbitals on Cl (Chlorine)

3sCl 3pzCl

3pxCl 3py

Cl

Hybride orbitals on H (Hydrogen)

1sA

Hybride orbitals on Cl (Chlorine)

σ−sp(B) :

12

[3s−3pz]

3pxCl 3py

Cl

Valence Bond Theory

A =1sH;B=σ+sp(Cl)

for σ-bond

Electron pairing and formation of bonds

ξ(1,2) =[A(1)B(2)+A(2)B(1)]×[α(1)β(2)−β(1)α(2)]

Electron pairing and formation oflone-pairs

A =σ−sp(Cl);B=σ−

sp(Cl)

for lone-pair

H Cl

H Cl

3pxCl

A = 3pxCl;B=3px

Cl

for lone-pair

H Cl

A = 3pyCl;B=3py

Cl

for lone-pair

3pyCl

H Cl

Atomic orbitals on Cl # 2

3sCl 3pzCl

3pxCl 3py

Cl

Cl Cl

Valence Bond Theory Applications

ξ(1,2) =[A(1)B(2)+A(2)B(1)]×[α(1)β(2)−β(1)α(2)]

Atomic orbitals on Cl # 1

3sCl 3pzCl

3pxCl 3py

Cl

Hybride orbitals on Cl # 1

3pxCl 3py

Clσ+sp(Cl) σ−

sp(Cl)

Hybride orbitals on Cl # 2

3pxCl 3py

Clσ+sp(Cl) σ−

sp(Cl)

Electron pairing and formation of bonds

Cl Cl

Valence Bond Theory Applicationsξ(1,2) =[A(1)B(2)+A(2)B(1)]×[α(1)β(2)−β(1)α(2)]

A =σ+sp(Cl1) ;B =σ+

sp(Cl2)

Cl Cl

σ−bond

Electron pairing and formation oflone-pairs

A =σ−sp(Cl1);B=σ−

sp(Cl1)

for lone-pair

Cl Cl

3pxCl

A= 3pxCl1;B=3px

Cl1

for lone-pair

Cl Cl

A = 3pyCl;B=3py

Cl

for lone-pair

3pyCl

Cl Cl

Same for Cl # 2

The orbital overlap and spin-pairing between electrons in two collinear p orbitals that result in the formation of a ( bond.

Valence Bond Theory Applications

ξ(1,2) =[A(1)B(2)+A(2)B(1)]×[α(1)β(2)−β(1)α(2)]

Valence Bond Theory Applications

ξ(1,2) =[A(1)B(2)+A(2)B(1)]×[α(1)β(2)−β(1)α(2)]

I. Diatomics

N N C O

A =σ+sp(1);B=σ+

sp(2)

for σ-bondσ+sp(1) :

12

[2s+2pz]

σ+sp(1) :

12

[2s−2pz]

A =σ−sp(1);B=σ−

sp(1)

for lone-pairs

A =2px1;B=2px

1

A =2py1;B=2py

1

π−bonds

Orbitals change signon reflexation in planecontaining 1-2 bond vector

Valence Bond Theory Applications

ξ(1,2) =[A(1)B(2)+A(2)B(1)]×[α(1)β(2)−β(1)α(2)]

I. Diatomics

The structure of bonds in a nitrogen molecule,which consists of one σ banda ndt woπ bands.

Theelect ron densi ty h ascylindrica l symmetryar ound th e internucle araxi .s

Valence Bond Theory Applications

CH C H

2. Linear molecules

A representation of the structure of a triple bond in ethyne; only the π bonds are shown explicitly. The overall electron density has cylindrical symmetry around the axis of the molecule.

Valence Bond Theory Applications3.Trigonal planar

C

H

H

C

H

HC2H4

C

H

H

O

CH2O

tr1

tr2

x

y

tr3

tr1 =13[s +px ]

tr2 =13[s −

12px +

32py ]

tr3 =13[s −

12px −

32py ]

C2H4

CH2O

Valence Bond Theory Applications

C

H

H

C

H

HC2H4

C2H4

(a) An s orbital and two p orbitals can behybridized to form three equivalent orbitalsthat point towards the corners of an equilateraltriangle. (b) The remaining, unhybridized porbital is perpendicular to the plane.

3.Trigonal planar

CH

H

H

H

X

y

z

t1

t2

t3

t4

Valence Bond Theory Applications

4.Tetrahedralt1 =

12[s +px +py +pz ]

( ,along x ,y )z

t2 =12[s −px −py +pz ]

(- ,along x- ,y )z

t3 =12[s −px +py −pz ]

(- ,along x ,y - )z

t4 =12[s +px −py −pz]

( ,along x- ,y - )z

sp3 −hybrides

An sp3 hybrid orbital formed from thesuperposition of s and p orbitals on the sameatom. There are four such hybrids: each onepoints towards the corner of a regulartetrahedron. The overall electron densityremains spherically symmetrical.

CH

H

H

H

Valence Bond Theory Applications

4.Tetrahedral sp3 −hybrides

A more detailed representation of theformation of an sp3 hybrid by interferencebetween wavefunctions centred on the sameatomic nucleus. (To simplify therepresentation, we have ignored the radialnode of the 2s orbital.)

CH

H

H

H

Valence Bond Theory Applications

4.Tetrahedral

sp3 −hybrides

= +

OH

H

NH

H

H

ξ(1,2) =[A(1)B(2)+A(2)B(1)]×[α(1)β(2)−β(1)α(2)]

Valence Bond Theory Applications

4.Tetrahedral

sp3 −hybrides

X

y

z

t1

t2

t3

t4

CH

H

H

H

X

y

z

t1

t2

t3

t4

X

y

z

t1

t2

t3

t4

A first approximation to the valence-bonddescription of bonding in an H2O molecule.Each σ bond ari sesfro m t he overl ap ofa 1n Hsorbita l wit h one o f th e 2O p orbitals. Thismode l sugge sts tha t t he bond ang leshoul d be90°, whi ch is significantl y differen t fro mtheexperimenta l value.

ξ(1,2) =[A(1)B(2)+A(2)B(1)]×[α(1)β(2)−β(1)α(2)]

Valence Bond Theory Applications

4.Tetrahedral sp3 −hybrides

OH

HX

y

z

t1

t2

t3

t4

use of sp3 −hybrides

Use of p - orbitals

Valence Bond Theory Applications

5.Bipyramidal d2sp2 −hybrides

PF

F

F

F

F

tr1 =13[s +px ]

tr2 =13[s −

12px +

32py ]

tr3 =13[s −

12px −

32py ]

tr1

tr2

x

y

tr3

d4 =12[pz +dz2 ]

d5 =12[pz −dz2 ]

d4

d5

z

SF

F

F

F

Valence Bond Theory Applications

5.Bipyramidald2sp2 −hybrides

PF

F

F

F

F S

F

F

F

F

ξ(1,2) =[A(1)B(2)+A(2)B(1)]×[α(1)β(2)−β(1)α(2)]

Valence Bond Theory Applications

6. Octahedral

d2sp3 −hybridesξ(1,2) =[A(1)B(2)+A(2)B(1)]×[α(1)β(2)−β(1)α(2)]

1

2

34

5

6 x

y

zoc1 =

16[s + 2d

z2+ 3pz ]

oc2 =16[s−

12dz2

+32dx2−y2

+ 3px ]

oc3 =16[s−

12dz2

−32dx2−y2

+ 3py ]

oc4 =16[s −

12dz2

+32dx2−y2

− 3px ]

oc5 =16[s −

12dz2

−32dx2−y2

− 3py ]

oc6 =16[s + 2d

z2− 3pz ]

Valence Bond Theory Applications

6. Octahedral

d2sp3 −hybridesξ(1,2) =[A(1)B(2)+A(2)B(1)]×[α(1)β(2)−β(1)α(2)]

x

y

z

SF

F

FF

F

F

What you should learn from this lecture

1. You are not required to know the mathematical form of the s and p atomic orbitals as well as

the sp,sp2,sp3,sp2d2,sp3d2 hybrides. However youshould be able to draw their shapes

2. You should be able to convert Lewis structures based on bonds and lone-pairs into valencebond pair functions ξ(1,2) =[A(1)B(2)+A(2)B(1)]×[α(1)β(2)−β(1)α(2)]where A and B are atomic orbitals (or hybrides)on different centersfor bonds ,and orbitals on the same center for lone-pairs